6. The hypotenuse of a right triangle is 20 cm. What is the maximum possible volume of the triangle in sq. cm

Answer 1

volume?
Area=1/2 b*h but 20^2=b^2+h^2 or
h=sqrt (400-b^2)
area= 1/2 * sqrt( )*b= 1/2 b*sqrt ( )
take the derivative, set darea/db =0, ans solve for b.

Answer 2

maximum area when the rectangle is a square, so that makes each side 20/√2
and the maximum area is thus 200 cm^2

Answer 3

Let
A=1/2 b x h
b^2 + h^2 = 20^2 → h = sqrt (400 - b^2)

Substitute h to A

A = (1/2)(b)sqrt(400-b^2)

Derive both sides and let dA/dt = 0
Find b

You can get b= 10sqrt(2)
Subs to h then you can get h=10sqrt(2)

A= 1/2 bxh
A=200/2
A=200 sq.cm

Answer 4

Correction for final answer:

A= 100 sq cm